Question

A random sample of 56 lithium batteries has a mean life of 645 hours with a population standard deviation of 31 hours. Compute the​ 95% confidence interval for mu. A. ​(636.9, 653.1) B. ​(712.0, 768.0) C. ​(539.6, 551.2) D. ​(112.0, 118.9)

Answer 1

Answer: A. ​(636.9, 653.1)

Step-by-step explanation:

Given : Sample size : n=56

Significance level :$\alpha: 1-0.95=0.05$

Critical value :$z_{0.05}=1.96$

Sample mean : $\overline{x}=645\text{ hours}$

Standard deviation : $\sigma= 31\text{ hours}$

The 95% confidence interval for population mean is given by :-

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=645\pm (1.96)\dfrac{31}{\sqrt{56}}\\\\=645\pm8.1\\\\=(636.9, 653.1)$

Hence,  95% confidence interval for population mean is (636.9, 653.1).